The Islamic State (IS), al-Qaeda-linked groups, Boko Haram and other extremist movements are protagonists in today’s deadliest crises, complicating efforts to end them. They have exploited wars, state collapse and geopolitical upheaval in the Middle East, gained new footholds in Africa and pose an evolving threat elsewhere. Reversing their gains requires avoiding the mistakes that enabled their rise. This means distinguishing between groups with different goals; using force more judiciously; ousting militants only with a viable plan for what comes next; and looking to open lines of communication, even with hardliners. Vital, too, is to de-escalate the crises they feed off and prevent others erupting, by nudging leaders toward dialogue, inclusion and reform and reacting sensibly to terrorist attacks. Most important is that action against “violent extremism” not distract from or deepen graver threats, notably escalating major- and regional-power rivalries.

The past quarter century has seen waves of jihadist violence: a first in the early 1990s, when volunteers from the anti-Soviet jihad in Afghanistan joined insurrections elsewhere; a second pioneered by al-Qaeda culminating in the 9/11 attacks; and a third sparked by the U.S. invasion of Iraq. Today’s fourth wave is the most perilous yet. Partly this is thanks to IS’s territorial control and ideological innovation – its tapping of both local Sunni and wider anti-establishment discontent. Mostly, though, it is dangerous because of the currents propelling it, particularly the Middle East’s upheaval and fraying state-society relations there and elsewhere. World leaders’ concern is well-founded: IS’s attacks kill their citizens and threaten their societies’ cohesion. They face enormous pressure to act. But they must do so prudently. Missteps – whether careless military action abroad; crackdowns at home; subordinating aid to counter-radicalisation; casting the net too wide; or ignoring severer threats in a rush to fight “violent extremism” – risk aggravating those deeper currents and again playing into jihadists’ hands.